All but 5 students in a certain calculus class took the final exam on

Question

All but 5 students in a certain calculus class took the final exam on the scheduled day. The mean score for these students was m. Later, the 5 students who had missed the scheduled exam took it and the mean score for the entire class was calculated. If n represents the mean score of the entire class, is n greater than m?

(1) The mode score for the entire class was higher than the mode score for the students who took the exam on the scheduled day.

(2) The range of the scores for the entire class was the same as the range of the scores for the students who took the exam on the scheduled day.

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Official Answer

E

saynchalk · Accepted Answer

Practice exam 3 for me

chetan2u · Answer

All but 5 students in a certain calculus class took the final exam on the scheduled day. The mean score for these students was m. Later, the 5 students who had missed the scheduled exam took it and the mean score for the entire class was calculated. If n represents the mean score of the entire class, is n greater than m?

Let the total strength be x, so total score of x-5 students = m(x-5).
Including these 5 students, total score is x*n.

So many unknowns and further unknowns in the statements.
x, m, n, mode, range??
Answer should be E because mean could have been compared if we had some substantial information such as total score, means etc

(1) The mode score for the entire class was higher than the mode score for the students who took the exam on the scheduled day.
Mode is the number(score) that comes the maximum number of times. So, the mode increases for all students.
Say, x=10 students, and 5 students on the scheduled day got score 10, 12, 12, 16, 20.
The entire class score could be = 10, 12, 12, 13, 13, 13, 14, 15, 16, 20....So, n<m
But it could also be 10, 12, 12, 16, 16, 16, 16, 16, 16, 20......n>m
Insuff

(2) The range of the scores for the entire class was the same as the range of the scores for the students who took the exam on the scheduled day.
Same examples would stand
Say, x=10 students, and 5 students on the scheduled day got score 10, 12, 12, 16, 20.
The entire class score could be = 10, 12, 12, 13, 13, 13, 14, 15, 16, 20....So, n<m
But it could also be 10, 12, 12, 16, 16, 16, 16, 16, 16, 20......n>m
Insuff

Combined
Say, x=10 students, and 5 students on the scheduled day got score 10, 12, 12, 16, 20.
The entire class score could be = 10, 12, 12, 13, 13, 13, 14, 15, 16, 20....So, n<m
But it could also be 10, 12, 12, 16, 16, 16, 16, 16, 16, 20......n>m
Insuff

E

GMATCoachBen · Answer

guddo  This one is from the official GMAT Focus practice exams? If so, do you know which exam number? Thanks!

guddo · Answer

GMATCoachBen

Yes, the question is from the new GMAT Prep Focus exams. You can see the screenshot in my initial post. However, I don't recall the specific exam number. It could be from any of them since I have access to all.

Aryaa03 · Answer

I got this in repeat of 3rd Mock.

sayan640 · Answer

MartyMurray   KarishmaB  Would you like to discuss this question ?

KarishmaB · Answer

Neither mode nor range can help us with the mean if we are adding 5 people. There are too many variations possible. I see that we are not given the number of students in the class either. So all I will do to convince myself that the answer is (E) is find a case in which the means are equal. Then a slight twist will establish insufficiency.

Say this is what the result of the class without the 5 looks like. Say mean is 30 (= m) and the mode is 30.
10 ..........................29, 30, 30, 31.......................... 50

Say these are the scores of the 5 students with higher mode of 31.
27, 28, 31, 31, 33

Then this is what the result of the entire class looks like. Mean n = 30, mode is 31, range is same 40.
10 ....................27, 28, 29, 30, 30, 31, 31, 31, 33 ........................... 50
(The mode score for the entire class was higher than the mode score for the students who took the exam on the scheduled day.)

Now if  I reduce the smallest score of the 5 students to 20, the mean n will reduce to less than 30.
But if I increase the greatest score of the 5 students to 40, the mean n will increase to more than 30. 
Hence n may be less than, equal to or greater than m.

Answer (E)

rajpatil.june · Answer

Visualization is the key here. So we need to answer question whether average of all class greater than subset of class? Visualize A The mode score for the entire class was higher than the mode score for the students who took the exam on the scheduled day. Mode of a new set is above average of subset then n>m, If mode is below average for original subset nm If the additional 5 numbers are below average of original subset n

anonymouslyyours · Answer

This question is from the GMAT official practice exam 3.

ablatt4 · Answer

Mode: most common result in a data set

Range: largest result - smallest result in a data set

Remember, the GMAT doesn't care about being realistic, this class could have had 6 students and could have had 12 million, both could be true within the confines of the question.

Statement 1 tells us the most common score was more common for the whole class than the 5 students, however the whole class could have mostly gotten a 0% and 100% so we have no idea how this effects the averages  insufficient

Statement 2 tells us about the range of the students, but again this could be a 1 point range from 0-1 and it could be a 100-point range, neither explain the mean at all.

Even together we have zero data relevant to either mean

E

Aboyhasnoname · Answer

There are just too many variables here.,....answer should be E...
We dont know the means of each group
we have some idea about mode...but how many times the mode is appearing to get the idea where mean will tilt....
we dont know the numbers in the group..total could be 6 or 6 million....

Anyway lets try to do it

Let the students who took the exam on scheduled date be called M..Their average is m  the students who took the exam later are 5 and their average is unknown   The average of M+5= n  
Statement 1.  Imagine there are 10 students in class..Their marks are as follows....  0,0 and the rest have 1,2,3,4,5,6,7,8 .... The average is 3.6.... Mode is 0   Case 1  5 students join...they have score 1,1,1,1,1 Mode of entire class becomes 1   the new average that is n will decrease here...How? Because the values added are less than the average..to keep the same we would have to add the same values as average......  Since the new values are less than the average ..the average comes down.....New average becomes ...41/15‎ = 2.733

n < m   Case 2.   5 students join they have score of 10,10,10,10,10  here the new mode of the entire class becomes 10..  and the average will come up...since values added are far above the mean.... 86/15 ‎ = 5.733  n > m   Insufficient    Statement 2.  case  10 students...Their scores are 0,0,0,0,1,1,1,2,2,2 -  Mode is 0  Average is 0.9 range is 2  5 students join their scores are 1,1,3,3,3  New mode is 1  Range is 2 New Average is 20/15‎ = 1.333 
n>m   10 students...Their scores are 0,0,0,0,1,1,1,2,2,2 -  Mode is 0  New Average is 0.9 range is 2 

5 students join their scores are 0,1,1,1,1 New mode becomes 1  Range is 2  New Average 13/15‎ = 0.867  here n < m    Insufficient   Combine also can take the same cases as in statement 2... 

quasipariatur · Answer

Yes it came in the exam

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